Development and individual differences in transitive reasoning: A fuzzy trace theory approach

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Abstract

Fuzzy trace theory explains why children do not have to use rules of logic or premise information to infer transitive relationships. Instead, memory of the premises and performance on transitivity tasks is explained by a verbatim ability and a gist ability. Until recently, the processes involved in transitive reasoning and memory of the premises were studied by comparing mean performance in fixed-age groups. In this study, an individual-difference model of fuzzy trace theory for transitive reasoning was formulated and tested on a sample (N = 409) of 4- to 13-year-old children. Tasks were used which differed with respect to presentation ordering and position ordering. From this individual-difference model expectations could be derived about the individual performance on memory and transitivity test-pairs.

The multilevel latent class model was used to fit the formalized individual-difference fuzzy trace theory to the sample data. The model was shown to fit the data to a large extent. The results showed that verbatim ability and gist ability drove the activation of verbatim and gist traces, respectively, and that children used combinations of these traces to solve memory tasks (testing memory of the premises) and transitivity tasks. Task format had a stronger effect on transitivity task performance than on memory of the premises. Development of gist ability was found to be faster than development of verbatim ability. Another important finding was that some children remembered the premise information correctly but were not able to infer the transitive relationship, even though the premises provided all the necessary information. This contradicts Trabasso’s linear ordering theory which posits that memory of the premises is sufficient to infer transitive relationships.

Section snippets

General introduction

A transitive reasoning task requires the inference of an unknown relationship between two objects from the known relationships between each of these objects and a third object. For example, let three sticks, A, B, and C, differ in length, denoted as Y, such that YA > YB > YC; then given YA > YB and YB > YC, the relationship between A and C can be inferred from these two relationships. In this example, the pairs [A, B] and [B, C] are the premise pairs and the relationships between the objects in the

Individual-difference model of fuzzy trace theory applied to transitive reasoning

In our individual-difference model of fuzzy trace theory, children’s performance on memory and transitivity test-pairs from a particular task is explained by the parallel retrieval and usage of verbatim and gist traces (Reyna & Brainerd, 1995a). Individual differences are explained from differences in the simultaneous use of verbatim and gist-trace levels. We assumed a verbatim ability and a gist ability on which children may differ. Tailored to transitive reasoning, verbatim ability refers to

Instrument

An individual computer test for transitive reasoning was constructed (Bouwmeester & Aalbers, 2004). Binary performance scores were registered automatically during test administration. Four test versions each presented the tasks in a different order. Each child was administered one randomly chosen version. The use of four versions was meant to rule out order effects due to task presentation. This was checked statistically by means of an ANOVA.

Sample

The transitive reasoning test was administered to 409

Alternative models for fuzzy trace theory

The individual-difference model of fuzzy trace theory is represented as Model A in Fig. 7. Other models were the following. Fuzzy trace theory assumes continuous verbatim and gist abilities, and discrete verbatim and gist traces each with three ordered levels. Model B is much simpler in that it lacks a latent variable structure. This model resembles an ANOVA on average scores for the three task types, and agrees with how Brainerd and Kingma, 1984, Brainerd and Kingma, 1985 tested their

Main findings

Fuzzy trace theory was used to explain individual differences in transitive reasoning. A model was set up in which verbatim and gist-ability levels governed the formation of verbatim and gist traces, and these traces governed performance on memory and transitivity test-pairs. Age was hypothesized to be related to both abilities. A multilevel latent class model was used to handle the dependencies between ability level and trace retrieval, and between trace retrieval and performance on the test

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